Quantization of Drinfeld Zastava in type C

TL;DR

This paper introduces a new quantization of the zastava space for symplectic Lie algebras, showing it is a quotient of the affine Borel Yangian, extending previous results from the finite case.

Contribution

It constructs a quantization of the zastava space for type C and proves it is a quotient of the affine Borel Yangian, linking geometric and algebraic structures.

Findings

The zastava space is isomorphic to a quiver variety in characteristic zero.

The quantization Y is a quotient of the affine Borel Yangian.

Results extend previous finite case work to affine symplectic Lie algebras.

Abstract

Drinfeld zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of an affine Lie algebra $\hat g$. In case $g$ is the symplectic Lie algebra $sp_N$, we introduce an affine, reduced, irreducible, normal quiver variety $Z$ which maps to the zastava space isomorphically in characteristic 0. The natural Poisson structure on the zastava space $Z$ can be described in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian reduction of the corresponding quotient of its universal enveloping algebra produces a quantization $Y$ of the coordinate ring of $Z$. The same quantization was obtained in the finite (as opposed to the affine) case generically in arXiv:math/0409031 . We prove that $Y$ is a quotient of the affine Borel Yangian. The analogous results for $g=sl_N$ were obtained in our previous work arXiv:1009.0676 .